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22                        ANALYTICAL MECHANICS
when the equiUbrium is disturbed and the body begins to slide down the plane. This angle is called the anylc oj friction. This definition for the angle of friction does not hold when the body is acted upon by other forces besides its weight and the reaction of the plane. The following definition, however, is valid under all circumstances: The angle of friction equals the angle which the total reaction wakes with the normal to the surface of contact when the body u on the point of motion.
28.   Coefficient of Friction.—Denoting the angle of friction
by <£, we obtain
F = R sin 0,
N = R cos 0.
Therefore                    F = N tan <£
= /JV,                                      (III)
where /* = tan <j> and is called the coefficient of friction. The angle of friction and consequently the coefficient of friction are constants which depend upon the surfaces in contact. The last four equations hold true only when the body is on the point of motion.
29.   Static and Kinetic Friction.—The friction which comes into play is called static friction if the body is at rest and kinetic friction if it is in motion.
30.   Laws of Friction. — The following statements, which are generalizations derived from experimental results, briiif? out the important properties of friction.   They hold true* wit hin certain limits and are only approximately true even within these limits.
1.   Frictional forces come into play only when a body is urged to move.
2.  Frictional forces always act in a direction opposite to that in which the body is urged to move.
3.   Frictional force is proportional to the normal reaction